Renardy, Michael Some remarks on the Navier-Stokes equations with a pressure-dependent viscosity. (English) Zbl 0597.35097 Commun. Partial Differ. Equations 11, 779-793 (1986). This paper studies existence, uniqueness and regularity for solutions to the Navier-Stokes equations, retaining the solenoidal restriction but allowing the viscosity to depend on pressure. Such situations, it is argued, are possible in motions of some organic liquids subjected to pressure variations of several thousand atmospheres. The pressure dependence of viscosity complicates the problem by allowing the equations to change type. However, it is shown that the Dirichlet boundary-initial value problem is well-posed provided the equations do not change type. Reviewer: B.Straugham Cited in 17 Documents MSC: 35Q30 Navier-Stokes equations 35R25 Ill-posed problems for PDEs 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:Navier-Stokes equations; solenoidal restriction PDF BibTeX XML Cite \textit{M. Renardy}, Commun. Partial Differ. Equations 11, 779--793 (1986; Zbl 0597.35097) Full Text: DOI OpenURL References: [1] DOI: 10.1002/cpa.3160170104 · Zbl 0123.28706 [2] DOI: 10.1063/1.1744583 [3] DOI: 10.1063/1.1744579 [4] Ladyzhenskaya O.A, Academic Press (1968) [5] DOI: 10.1016/0022-0396(83)90013-X · Zbl 0476.35032 [6] Smoller J, Springer (1983) [7] Sobolevskii P.E, AmerMath. Soc. Transl 49 pp 1– (1966) [8] Stokes G.G., Trans. Cambridge phil.soc. 8 pp 287– (1845) [9] Temam, R. 1979. ”Navier-Stokes Equations”. North Holland · Zbl 0426.35003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.